System Description: LEO - A Higher-Order Theorem Prover

  title={System Description: LEO - A Higher-Order Theorem Prover},
  author={Christoph Benzm{\"u}ller and Michael Kohlhase},
Many (mathematical) problems, such as Cantor’s theorem, can be expressed very elegantly in higher-order logic, but lead to an exhaustive and un-intuitive formulation when coded in first-order logic. Thus, despite the difficulty of higher-order automated theorem proving, which has to deal with problems like the undecidability of higher-order unification (HOU) and the need for primitive substitution, there are proof problems which lie beyond the capabilities of first-order theorem provers, but… 
Equality and extensionality in automated higher order theorem proving
The three new calculi ER, ERUE, EP and ERUE which improve the mechanisation of defined and primitvie equality in classical type theory and these calculi reach Henkin completeness without requiring additional extensionality axioms are introduced.
Extensional Higher-Order Paramodulation in Leo-III
Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice that supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.
An Adaptation of Paramodulation and Rue-resolution to Higher-order Logic
This techreport presents two approaches to primitive equality treatment in higher-order (HO) automated theorem proving: a calculus EP adapting traditional rst-order (FO) paramodulation RW69] , and a
Can a Higher-Order and a First-Order Theorem Prover Cooperate?
This work has shown in the past that higher-order reasoning systems can solve problems of this kind automatically, but the complexity inherent in their calculi and their inefficiency in dealing with large numbers of clauses prevent these systems from solving a whole range of problems.
System Description: LEO -- A Resolution based Higher-Order Theorem Prover
The Leo system has recently been successfully coupled with a first-order resolution theorem prover (Bliksem) and is implemented as part of the Ωmega environment and has been integrated with theΩmega proof assistant.
Extensional Higher-Order Paramodulation and RUE-Resolution
Two approaches to primitive equality treatment in higher-order (HO) automated theorem proving are presented: a calculus EP adapting traditional first-orders paramodulation, and a calculus ERUE adapting FO RUE-Resolution to classical type theory, i.e., HO logic based on Church's simply typed λ-calculus.
A Lost Proof
We re-investigate a proof example presented by George Boolos which perspicuously illustrates Gödel’s argument for the potentially drastic increase of proof-lengths in formal systems when carrying
LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description)
The improved performance of LEO-II, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level.
Fast Clause Normalization for Higher-Order Automated Theorem Proving
The task is to develop a new and ideally improved OANTS architecture for the new LEO-II prover, which is currently using a primitive, sequential interaction model.
Functions-as-Constructors Higher-Order Unification
The main idea behind this extension is that the arguments to a higher-order, free variable can be more than just distinct bound variables: they can also be terms constructed from (sufficient numbers of) such variables using term constructors and where no argument is a subterm of any other argument.


A mechanization of sorted higher-order logic based on the resolution principle
This thesis develops a sorted higher-order logic SUM HOL suitable for automatic theorem proving applications, and develops two notions of set-theoretic semantics for SUM HOL, which generalize general SUM-models further to SUM-model structures, which allow full extensionality to fail.
A calculus and a system architecture for extensional higher-order resolution
The first part of this paper introduces an extension for a variant of Huet's higher-order resolution calculus [Hue72, Hue73] based upon classical type theory (Church's typed A-calculus [Chu40]) in
A Calculus and a System Architecture for Extensional Higher-Order Resolution
The first part of this paper introduces an extension for a variant of Huet's higher-order resolution calculus [Hue72, Hue73] based upon classical type theory (Church's typed A-calculus [Chu40]) in
Extensional Higher-Order Resolution
An extensional higher-order resolution calculus that is complete relative to Henkin model semantics is presented and the long-standing conjecture, that it is sufficient to restrict the order of primitive substitutions to the orders of input formulae is proved.
A Unification Algorithm for Typed lambda-Calculus
  • G. Huet
  • Computer Science
    Theor. Comput. Sci.
  • 1975
Term Indexing
Reading term indexing is also a way as one of the collective books that gives many advantages, not only for you, but for the other peoples with those meaningful benefits.
Unification Under a Mixed Prefix
Boolean Properties of Sets
Summary. The text includes a number of theorems about Boolean operations on sets: union, intersection, difference, symmetric difference; and relations on sets: meets (having non-empty intersection),
KEIM: A Toolkit for Automated Deduction
KEIM is a collection of software modules, written in Common Lisp with CLOS, designed to be used in the implementation of automated reasoning systems, offering a range of datatypes implementing a logical language of type theory (higher order logic), in which first order logic can be easily embedded.
Proc. CADE-15, this volume
  • Proc. CADE-15, this volume
  • 1998